$J$ $K$ $L$ If: $ KL = 7x + 8$, $ JL = 55$, and $ JK = 4x + 3$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {4x + 3} + {7x + 8} = {55}$ Combine like terms: $ 11x + 11 = {55}$ Subtract $11$ from both sides: $ 11x = 44$ Divide both sides by $11$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $KL$ $ KL = 7({4}) + 8$ Simplify: $ {KL = 28 + 8}$ Simplify to find ${KL}$ : $ {KL = 36}$